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Question Number 53528 by naka3546 last updated on 22/Jan/19

x^3  + y^3  + z^3   =  x + y + z  x^2  + y^2  + z^2   =  xyz  x, y, z  ∈ R^+   How  many  triple  of  (x, y, z)  ?

$${x}^{\mathrm{3}} \:+\:{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \:\:=\:\:{x}\:+\:{y}\:+\:{z} \\ $$$${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \:\:=\:\:{xyz} \\ $$$${x},\:{y},\:{z}\:\:\in\:\mathbb{R}^{+} \\ $$$${How}\:\:{many}\:\:{triple}\:\:{of}\:\:\left({x},\:{y},\:{z}\right)\:\:? \\ $$

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